Question 917391
Let m = how many days 1 man could do the work if alone;
let w = how many ways 1 woman could do the same work alone.


{{{cross((8(1/m)+16(1/w))40=1)}}} and {{{cross((40(1/m)+48(1/w))2=1)}}}


Two equations, two unknown variables; simplify each equation and solve the system.


The first arrangement of workers
{{{(8/m+16/w)8=1}}} to account for 1 job
{{{64/m+128/w=1}}}, and LCD is mw
{{{64w+128m=mw}}}


Second arrangement of workers
{{{(40/m+48/w)2=1}}}
{{{80/m+96/w=1}}}
{{{80w+96m=mw}}}


Two equal formulas for mw.
{{{64w+128m=80w+96m}}}
{{{32m=16w}}}
{{{2m=w}}}
This is the relationship between m and w, which through substitution,
allows to find through either of the mw equations, to solve for w and m,
the NUMBER OF DAYS for one woman to do one job and the NUMBER OF DAYS for one man to do one job.


Use this system:
{{{highlight_green(system(64w+128m=mw,90w+96m=mw,w=2m))}}}


(Further steps, not yet done, but you need to do them.)


You can then answer the actual question from there, using RT=J for 
rate time job, uniform work rates formula. 


Substituting {{{w=2m}}} in the {{{64w+128m=mw}}}, solving for m gives
{{{highlight(m=128)}}} days and this means {{{highlight(w=256)}}} days.


Now, use those to solve the question asked.



Rate in jobs per day for the 6 men and 12 women,
{{{(6/128+12/256)}}}


Let t be the number of days for this group to do 1 job.
The uniform rates rule gives:
{{{highlight((6/128+12/256)t=1)}}}
Solve for t.
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RESULT:  {{{highlight(t=10&2/3)}}} days.